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scores_loc <- read.table("/Users/jialincheoh/Downloads/overall_score_click_result.csv", header=TRUE, sep = ",")
scores_loc

scores_novelty <- scores_loc[, c('Group', 'novelty.phase5')]
scores_novelty                         

library(onewaytests)
charac <- as.character(scores_novelty$Group)
bf.test(novelty.phase5 ~ charac, scores_novelty)

  Brown-Forsythe Test (alpha = 0.05) 
------------------------------------------------------------- 
  data : novelty.phase5 and charac 

  statistic  : 1.05192 
  num df     : 3 
  denom df   : 159.3847 
  p.value    : 0.3713216 

  Result     : Difference is not statistically significant. 
------------------------------------------------------------- 

lmnovelty <- lm(novelty.phase5 ~ Group, scores_novelty)
plot(lmnovelty)

lmtest::bptest(lmnovelty)  

    studentized Breusch-Pagan test

data:  lmnovelty
BP = 0.12658, df = 1, p-value = 0.722

car::ncvTest(lmnovelty)  

Non-constant Variance Score Test 
Variance formula: ~ fitted.values 
Chisquare = 0.0376888, Df = 1, p = 0.84607

# Not normal which is a BIG problem
shapiro.test(residuals(lmnovelty))

    Shapiro-Wilk normality test

data:  residuals(lmnovelty)
W = 0.91828, p-value = 5.659e-08

Assumptions. Student’s t-test assumes that the population parameter being compared for two populations is normally distributed, and that the populations have equal variances. Welch’s t-test is designed for unequal population variances, but the assumption of normality is maintained.

scores_novelty$novelty.phase5[scores_novelty$novelty.phase5==0] <- 0.00000000001

library(MASS)
bcmle <- boxcox(lm(novelty.phase5~Group, data=scores_novelty), lambda=seq(-3, 3, by=0.1))

lambda<-bcmle$x[which.max(bcmle$y)]
lambda

[1] 0.09090909

scores_novelty$novelty.phase5

  [1] 5.0000e+01 6.7500e+01 2.5000e+01 1.6670e+01 8.7500e+01 5.0000e+01 1.0000e-11 6.0000e+01 6.6670e+01 6.8750e+01 6.2500e+01
 [12] 5.2500e+01 6.6670e+01 1.0000e-11 2.5000e+01 7.5000e+01 2.5000e+01 2.5000e+01 7.5000e+01 1.0000e-11 8.7500e+01 1.0000e-11
 [23] 2.5000e+01 7.5000e+01 3.7500e+01 2.5000e+01 6.2500e+01 7.5000e+01 1.0000e-11 1.0625e+02 7.5000e+01 5.8330e+01 1.0000e-11
 [34] 1.0000e-11 1.0000e-11 1.0000e-11 1.0000e-11 1.0000e-11 1.0000e-11 2.5000e+01 1.0000e-11 6.2500e+01 1.0000e-11 2.5000e+01
 [45] 1.0000e-11 2.5000e+01 6.2500e+01 1.0000e+02 1.0000e-11 8.2500e+01 8.7500e+01 6.2500e+01 7.7500e+01 8.2500e+01 7.0000e+01
 [56] 5.0000e+01 9.1670e+01 5.6250e+01 8.5000e+01 8.7500e+01 2.5000e+01 1.0000e-11 5.0000e+01 1.0000e-11 7.5000e+01 8.7500e+01
 [67] 7.5000e+01 2.5000e+01 5.2500e+01 6.2500e+01 1.0000e-11 6.6670e+01 7.2500e+01 9.5000e+01 8.1250e+01 2.5000e+01 1.0000e-11
 [78] 1.0000e-11 1.0000e-11 1.0000e-11 1.0000e-11 1.0000e-11 2.5000e+01 2.5000e+01 8.0000e+01 8.7500e+01 7.5000e+01 2.5000e+01
 [89] 2.5000e+01 1.0000e-11 6.2500e+01 2.5000e+01 6.6670e+01 8.7500e+01 6.0000e+01 2.5000e+01 6.5000e+01 8.4380e+01 7.2500e+01
[100] 1.0000e-11 6.2500e+01 6.2500e+01 1.0000e+02 3.7500e+01 2.5000e+01 7.5000e+01 2.5000e+01 1.0000e-11 7.5000e+01 1.0000e-11
[111] 6.2500e+01 7.5000e+01 6.5630e+01 1.0000e+02 2.5000e+01 3.3330e+01 1.2500e+01 7.0000e+01 1.0000e-11 1.0000e-11 1.0000e-11
[122] 1.0000e-11 8.7500e+01 9.2500e+01 1.5000e+01 5.6250e+01 2.5000e+01 9.5000e+01 1.0000e-11 1.0000e-11 7.2500e+01 5.6250e+01
[133] 2.5000e+01 2.5000e+01 6.0000e+01 1.0000e+02 8.1250e+01 5.0000e+01 6.6670e+01 7.5000e+01 3.7500e+01 5.0000e+01 6.7500e+01
[144] 5.8330e+01 2.5000e+01 2.5000e+01 1.0000e-11 8.1250e+01 8.7500e+01 1.2500e+01 5.6250e+01 9.3750e+01 5.7500e+01 5.6250e+01
[155] 1.0000e-11 8.3330e+01 5.7500e+01 8.1250e+01 9.0000e+01 7.5000e+01 1.0000e-11 1.0000e-11 1.0000e-11 1.0000e-11

fullmodel.inv = lm((novelty.phase5)^0.1010101 ~ Group, data=scores_novelty )
plot(fullmodel.inv)

NA

shapiro.test(residuals(fullmodel.inv))

    Shapiro-Wilk normality test

data:  residuals(fullmodel.inv)
W = 0.68977, p-value < 2.2e-16

summary(lmnovelty)

Call:
lm(formula = novelty.phase5 ~ Group, data = scores_novelty)

Residuals:
    Min      1Q  Median      3Q     Max 
-49.629 -37.759   7.024  28.697  66.600 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   39.650      4.410   8.990 6.19e-16 ***
Group          3.327      2.349   1.416    0.159    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 33.47 on 162 degrees of freedom
Multiple R-squared:  0.01223,   Adjusted R-squared:  0.006129 
F-statistic: 2.005 on 1 and 162 DF,  p-value: 0.1587

lmtotal <- lm(total.phase5 ~ Group, scores_loc)
summary(lmtotal)

Call:
lm(formula = total.phase5 ~ Group, data = scores_loc)

Residuals:
     Min       1Q   Median       3Q      Max 
-217.188  -80.067    6.134  100.438  188.822 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  164.098     14.303  11.473   <2e-16 ***
Group         17.697      7.619   2.323   0.0214 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 108.5 on 162 degrees of freedom
Multiple R-squared:  0.03223,   Adjusted R-squared:  0.02625 
F-statistic: 5.395 on 1 and 162 DF,  p-value: 0.02144

lmtotal <- lm(total.phase5 ~ Group, scores_loc)
summary(lmtotal)

Call:
lm(formula = total.phase5 ~ Group, data = scores_loc)

Residuals:
     Min       1Q   Median       3Q      Max 
-217.188  -80.067    6.134  100.438  188.822 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  164.098     14.303  11.473   <2e-16 ***
Group         17.697      7.619   2.323   0.0214 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 108.5 on 162 degrees of freedom
Multiple R-squared:  0.03223,   Adjusted R-squared:  0.02625 
F-statistic: 5.395 on 1 and 162 DF,  p-value: 0.02144

plot(lmtotal)

shapiro.test(residuals(lmtotal))

    Shapiro-Wilk normality test

data:  residuals(lmtotal)
W = 0.95955, p-value = 0.0001067

 wilcox.test(scores_loc$total.phase5, scores_loc$Group, data=bogota_23) 

    Wilcoxon rank sum test with continuity correction

data:  scores_loc$total.phase5 and scores_loc$Group
W = 24664, p-value < 2.2e-16
alternative hypothesis: true location shift is not equal to 0

 wilcox.test(scores_loc$Group, scores_loc$novelty.phase5) 

    Wilcoxon rank sum test with continuity correction

data:  scores_loc$Group and scores_loc$novelty.phase5
W = 5904, p-value < 2.2e-16
alternative hypothesis: true location shift is not equal to 0

 wilcox.test(scores_loc$Group, scores_loc$user.requirement.phase5) 

    Wilcoxon rank sum test with continuity correction

data:  scores_loc$Group and scores_loc$user.requirement.phase5
W = 6048, p-value < 2.2e-16
alternative hypothesis: true location shift is not equal to 0

 wilcox.test(scores_loc$Group, scores_loc$tech.phase5) 

    Wilcoxon rank sum test with continuity correction

data:  scores_loc$Group and scores_loc$tech.phase5
W = 3312, p-value < 2.2e-16
alternative hypothesis: true location shift is not equal to 0

pairwise.wilcox.test(scores_loc$total.phase5, scores_loc$Group,
                 p.adjust.method = "BH")

Warning in wilcox.test.default(xi, xj, paired = paired, ...) :
  cannot compute exact p-value with ties
Warning in wilcox.test.default(xi, xj, paired = paired, ...) :
  cannot compute exact p-value with ties
Warning in wilcox.test.default(xi, xj, paired = paired, ...) :
  cannot compute exact p-value with ties
Warning in wilcox.test.default(xi, xj, paired = paired, ...) :
  cannot compute exact p-value with ties
Warning in wilcox.test.default(xi, xj, paired = paired, ...) :
  cannot compute exact p-value with ties
Warning in wilcox.test.default(xi, xj, paired = paired, ...) :
  cannot compute exact p-value with ties

    Pairwise comparisons using Wilcoxon rank sum test with continuity correction 

data:  scores_loc$total.phase5 and scores_loc$Group 

  0    1    2   
1 0.33 -    -   
2 0.33 0.93 -   
3 0.11 0.37 0.33

P value adjustment method: BH 

kruskal.test(total.phase5 ~ Group, data = scores_loc)

    Kruskal-Wallis rank sum test

data:  total.phase5 by Group
Kruskal-Wallis chi-squared = 5.949, df = 3, p-value = 0.1141

bogota_23 <- scores_loc[ which( scores_loc$Group == 2 | scores_loc$Group == 3) , ]
bogota_23

kruskal.test(novelty.phase5 ~ Group, data = bogota_23)

    Kruskal-Wallis rank sum test

data:  novelty.phase5 by Group
Kruskal-Wallis chi-squared = 0.85845, df = 1, p-value = 0.3542

 wilcox.test(bogota_23$Group, bogota_23$total.phase5) 

    Wilcoxon rank sum test with continuity correction

data:  bogota_23$Group and bogota_23$total.phase5
W = 581, p-value < 2.2e-16
alternative hypothesis: true location shift is not equal to 0

library(AID)
library(onewaytests)
nor.test(novelty.phase5 ~ charac, data = scores_loc) 

  Shapiro-Wilk Normality Test (alpha = 0.05) 
-------------------------------------------------- 
  data : novelty.phase5 and charac 

-------------------------------------------------- 

homog.test(total.phase5 ~ charac, data = scores_loc, method = "Fligner")

  Fligner-Killeen Homogeneity Test (alpha = 0.05) 
--------------------------------------------------- 
  data : total.phase5 and charac 

  statistic  : 0.3248996 
  parameter  : 3 
  p.value    : 0.9552795 

  Result     : Variances are homogeneous. 
--------------------------------------------------- 

scores_loc$total.phase5[scores_loc$total.phase5==0] <- 0.00000000001

out <- boxcoxfr(scores_loc$novelty.phase5, scores_loc$Group) 

zero <- scores_loc[scores_loc$total.phase5 != 0.00000000001, ]
zero

lmtotal_revise <- lm(total.phase5 ~ Group, data=zero)
plot(lmtotal_revise)

library(AID)
library(onewaytests)
nor.test(total.phase5 ~ as.character(Group), data = zero) 

  Shapiro-Wilk Normality Test (alpha = 0.05) 
-------------------------------------------------- 
  data : total.phase5 and as.character(Group) 

-------------------------------------------------- 

homog.test(total.phase5 ~ as.character(Group), data = zero, method = "Fligner")

  Fligner-Killeen Homogeneity Test (alpha = 0.05) 
--------------------------------------------------- 
  data : total.phase5 and as.character(Group) 

  statistic  : 2.606498 
  parameter  : 3 
  p.value    : 0.4563514 

  Result     : Variances are homogeneous. 
--------------------------------------------------- 

out <- boxcoxfr(zero$total.phase5, zero$Group) 

Error in boxcoxfr(zero$total.phase5, zero$Group) : 
  Feasible region is null set. No solution. 
  Try to enlarge the range of feasible lambda values, lambda. 
  Try to decrease feasible region parameter, tau.

result<-aov.test(total.phase5 ~ as.character(Group), data = zero) 

  One-Way Analysis of Variance (alpha = 0.05) 
------------------------------------------------------------- 
  data : total.phase5 and as.character(Group) 

  statistic  : 1.025466 
  num df     : 3 
  denom df   : 142 
  p.value    : 0.3833417 

  Result     : Difference is not statistically significant. 
------------------------------------------------------------- 

pairwise.wilcox.test(zero$total.phase5, zero$Group,
                 p.adjust.method = "BH")

Warning in wilcox.test.default(xi, xj, paired = paired, ...) :
  cannot compute exact p-value with ties
Warning in wilcox.test.default(xi, xj, paired = paired, ...) :
  cannot compute exact p-value with ties
Warning in wilcox.test.default(xi, xj, paired = paired, ...) :
  cannot compute exact p-value with ties
Warning in wilcox.test.default(xi, xj, paired = paired, ...) :
  cannot compute exact p-value with ties
Warning in wilcox.test.default(xi, xj, paired = paired, ...) :
  cannot compute exact p-value with ties
Warning in wilcox.test.default(xi, xj, paired = paired, ...) :
  cannot compute exact p-value with ties

    Pairwise comparisons using Wilcoxon rank sum test with continuity correction 

data:  zero$total.phase5 and zero$Group 

  0    1    2   
1 0.71 -    -   
2 0.71 0.93 -   
3 0.51 0.51 0.51

P value adjustment method: BH 

kruskal.test(total.phase5 ~ Group, data = zero)

    Kruskal-Wallis rank sum test

data:  total.phase5 by Group
Kruskal-Wallis chi-squared = 3.2169, df = 3, p-value = 0.3594

wilcox.test(bogota_23$total.phase5, bogota_23$Group)$p.value

[1] 5.729537e-21

wilcox.test(bogota_23$novelty.phase5, bogota_23$Group)$p.value

[1] 2.438505e-11

wilcox.test(bogota_23$user.requirement.phase5, bogota_23$Group)$p.value

[1] 4.279913e-09

wilcox.test(bogota_23$infovis.phase5, bogota_23$Group)$p.value

[1] 5.408198e-21

# Plot weight by group and color by group
library("ggpubr")
ggboxplot(bogota_23, x = "Group", y = "total.phase5", 
          color = "Group",
          ylab = "total.phase5", xlab = "Group")

# Plot weight by group and color by group
library("ggpubr")
ggboxplot(bogota_23, x = "Group", y = "total.phase5", 
          color = "Group",
          ylab = "total.phase5", xlab = "Group")

# Plot weight by group and color by group
library("ggpubr")
ggboxplot(bogota_23, x = "Group", y = "novelty.phase5", 
          color = "Group",
          ylab = "novelty.phase5", xlab = "Group")

# Plot weight by group and color by group
library("ggpubr")
ggboxplot(bogota_23, x = "Group", y = "user.requirement.phase5", 
          color = "Group",
          ylab = "user.requirement.phase5", xlab = "Group")

# Plot weight by group and color by group
library("ggpubr")
ggboxplot(bogota_23, x = "Group", y = "tech.phase5", 
          color = "Group",
          ylab = "tech.phase5", xlab = "Group")

# Plot weight by group and color by group
library("ggpubr")

Loading required package: ggplot2

ggboxplot(bogota_23, x = "Group", y = "infovis.phase5",
          color = "Group",
          ylab = "infovis.phase5", xlab = "Group")

kruskal.test( novelty.phase5 ~ Group, data = bogota_23)

    Kruskal-Wallis rank sum test

data:  novelty.phase5 by Group
Kruskal-Wallis chi-squared = 0.85845, df = 1, p-value = 0.3542

kruskal.test( total.phase5 ~ Group, data = bogota_23)

    Kruskal-Wallis rank sum test

data:  total.phase5 by Group
Kruskal-Wallis chi-squared = 1.5356, df = 1, p-value = 0.2153

bogota_23

bogota_23$novelty.phase5[bogota_23$novelty.phase5==0] <- 0.00000000001

library(MASS)
bcmle <- boxcox(lm(novelty.phase5~Group, data=bogota_23), lambda=seq(-3, 3, by=0.1))
lambda<-bcmle$x[which.max(bcmle$y)]
lambda

fullmodel.inv = lm((novelty.phase5)^0.1515 ~ Group, data=bogota_23 )
plot(fullmodel.inv)

shapiro.test(residuals(fullmodel.inv))

shapiro.test(residuals(lm(novelty.phase5 ~ Group, data=bogota_23)))

shapiro.test(residuals(lm(total.phase5 ~ Group, data=bogota_23)))

# Plot weight by group and color by group
library("ggpubr")
ggboxplot(bogota_23, x = "Group", y = "tech.phase5", 
          color = "Group",
          ylab = "tech.phase5", xlab = "Group")

bogota_23$infovis.phase5

kruskal.test( novelty.phase5 ~ Group, data = bogota_23)